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Register a new userParquet decomposition calculations of the electronic self-energy
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The parquet decomposition of the self-energy into classes of diagrams, those associated with specific scattering processes, can be exploited for different scopes. In this work, the parquet decomposition is used to unravel the underlying physics of non-perturbative numerical calculations. We show the specific example of dynamical mean field theory (DMFT) and its cluster extensions (DCA) applied to the Hubbard model at half-filling and with hole doping: These techniques allow for a simultaneous determination of two-particle vertex functions and self-energies, and hence, for an essentially exact parquet decomposition at the single-site or at the cluster level. Our calculations show that the self-energies in the underdoped regime are dominated by spin scattering processes, consistent with the conclusions obtained by means of the fluctuation diagnostics approach [Phys. Rev. Lett. 114, 236402 (2015)]. However, differently from the latter approach, the parquet procedure displays important changes with increasing interaction: Even for relatively moderate couplings, well before the Mott transition, singularities appear in different terms, with the notable exception of the predominant spin-channel. We explain precisely how these singularities, which partly limit the utility of the parquet decomposition, and - more generally - of parquet-based algorithms, are never found in the fluctuation diagnostics procedure. Finally, by a more refined analysis, we link the occurrence of the parquet singularities in our calculations to a progressive suppression of charge fluctuations and the formation of an RVB state, which are typical hallmarks of a pseudogap state in DCA.
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We exploit the parquet formalism to derive exact flow equations for the two-particle-reducible four-point vertices, the self-energy, and typical response functions, circumventing the reliance on higher-point vertices. This includes a concise, algebraic derivation of the multiloop flow equations, which have previously been obtained by diagrammatic considerations. Integrating the multiloop flow for a given input of the totally irreducible vertex is equivalent to solving the parquet equations with that input. Hence, one can tune systems from solvable limits to complicated situations by variation of one-particle parameters, staying at the fully self-consistent solution of the parquet equations throughout the flow. Furthermore, we use the resulting differential form of the Schwinger-Dyson equation for the self-energy to demonstrate one-particle conservation of the parquet approximation and to construct a conserving two-particle vertex via functional differentiation of the parquet self-energy. Our analysis gives a unified picture of the various many-body relations and exact renormalization group equations.
The correlated electronic structure of SrVO3 has been investigated by angle-resolved photoemission spectroscopy using in-situ prepared thin films. Pronounced features of band renormalization have been observed: a sharp kink ~60 meV below the Fermi level (EF) and a broad so-called high-energy kink ~0.3 eV below EF as in the high-Tc cuprates although SrVO3 does not show magnetic fluctuations. We have deduced the self-energy in a wide energy range by applying the Kramers-Kronig relation to the observed spectra. The obtained self-energy clearly shows a large energy scale of ~0.7 eV which is attributed to electron-electron interaction and gives rise to the ~0.3 eV kink in the band dispersion as well as the incoherent peak ~1.5eV below EF. The present analysis enables us to obtain consistent picture both for the incoherent spectra and the band renormalization.
We propose a systematic procedure for constructing effective models of strongly correlated materials. The parameters, in particular the on-site screened Coulomb interaction U, are calculated from first principles, using the GW approximation. We derive an expression for the frequency-dependent U and show that its high frequency part has significant influence on the spectral functions. We propose a scheme for taking into account the energy dependence of U, so that a model with an energy-independent local interaction can still be used for low-energy properties.
The LDA+DMFT method is a very powerful tool for gaining insight into the physics of strongly correlated materials. It combines traditional ab-initio density-functional techniques with the dynamical mean-field theory. The core aspects of the method are (i) building material-specific Hubbard-like many-body models and (ii) solving them in the dynamical mean-field approximation. Step (i) requires the construction of a localized one-electron basis, typically a set of Wannier functions. It also involves a number of approximations, such as the choice of the degrees of freedom for which many-body effects are explicitly taken into account, the scheme to account for screening effects, or the form of the double-counting correction. Step (ii) requires the dynamical mean-field solution of multi-orbital generalized Hubbard models. Here central is the quantum-impurity solver, which is also the computationally most demanding part of the full LDA+DMFT approach. In this chapter I will introduce the core aspects of the LDA+DMFT method and present a prototypical application.
We investigate the antiferromagnetic insulating nature of Ca3FeRhO6 both experimentally and theoretically. Susceptibility measurements reveal a Neel temperature T_N = 20 K, and a magnetic moment of 5.3 muB/f. u., while Moessbauer spectroscopy strongly suggests that the Fe ions, located in trigonal prismatic sites, are in a 3+ high spin state. Transport measurements display a simple Arrhenius law, with an activation energy of 0.2 eV. The experimental results are interpreted with LSDA band structure calculations, which confirm the Fe 3+ state, the high-spin/low-spin scenario, the antiferromagnetic ordering, and the value for the activation energy.
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